Morphy number 1

Morphy is known to have played about 100 people, but all of the known links for players with Morphy number 2 go through the following five players.^[1][4]

A few years after the early lists of Morphy numbers tabulated, it was discovered that a fifth player, James Mortimer, was Morphy's friend and he played casual games with him. This gives Mortimer a Morphy number of 1, creating a need to drastically revise those previous lists to include many more players.^[4][5] This is because Mortimer had a very long, if not particularly successful, career, including the Ostende-B 1907 tournament. This enabled many famous younger players to gain a Morphy number of 2, including Mieses, Tartakower, Znosko-Borovsky, and Bernstein, who played beyond WW2, enabling still younger players to gain a Morphy number of 3, and so on.

Morphy number 2

Everyone in this group played someone in the group above. The Australian champion Frederick Esling achieved MN2 by beating Anderssen in an offhand game^[6] and another Australian champion, Julius Leigh Jacobsen (1862–1916)^[7] achieved MN2 by beating Bird in a casual match +4-2=1, enabling many Australian players of the early 20th century to achieve MN3.^[8] The following are some of the most important players who have achieved MN2.^[1]

Morphy number 3

Most of the masters in this group played several members of the previous group. This group includes some of the most important players for making connections to later generations. Botvinnik and Reshevsky played older masters such as Lasker and Janowski, had long careers, and played many younger players.^[1] Najdorf was Tartakower's pupil and they played a number of published games together, and Najdorf played blitz right into his 80s, allowing many younger players to achieve 4. Smyslov and Keres had very long careers, so much younger players achieved MN4 by playing them. Gligoric also played Tartakover,^[17] allowing many Yugoslav players to achieve 4. C.J.S. Purdy played Tartakower,^[18] enabling many Australian players to achieve 4. Fairhurst, who played Tartakover,^[19] was many times champion of Scotland, and later moved to New Zealand, so a number of players in these countries achieved 4 by playing him.

As of August 2023, living players with Morphy number 3 are Leonard Barden, Bernard Cafferty, Owen Hindle, Franciscus Kuijpers, Christian Langeweg, Friðrik Ólafsson, Oliver Penrose, Stewart Reuben and Jim Walsh.^{[4][20][21][22][23]}

Morphy number 4

As of 2013^[update] many of these players are still alive; a few (such as Anand, Adams, Nakamura, Svidler and Ivanchuk) are still active.^[1]

Morphy number 5

As of 2013^[update], many of the top grandmasters were thought to be in this group (along with a large number of lower-rated players).^[1] However, several players initially thought to be in this group were actually MN4s;^[53] for instance, based on playing Smyslov, who played Tartakower and Bernstein.